Assigning Equity to Investors / Structuring

Been searching a few months now, and one question I keep running into (with no clear answer thus far) is the actual mechanics of assigning equity to investors and how this interacts with a searcher's choice of entities.

It's clear that many, if not most, self-funded searchers (of which I am one) form an LLC as the search vehicle. I've done this part recently. Where I am a little lost is how this interacts with the later purchase of a target company. I will be raising some amount of equity from investors. From what I can understand, typically those investors would be offered a preferred return, and some common equity.

2 big questions then: 1) Isn't a C Corp needed for the equity issuance / management? 2) What exactly is the use of the LLC search vehicle then - is it a good idea to have simply for expenses, is it designed to be restructured as a C Corp at the time of acquisition, should I just ensure the acquisition is a C Corp, does it make sense in the first place for the search vehicle to be the entity purchasing the acquisition?

Would appreciate if someone can answer these questions clearly. Thanks!